Asymptotics of the 1D compressible Navier-Stokes equations with density-dependent viscosity

DOI10.1016/j.jde.2019.12.029zbMath1433.35221OpenAlexW2999607466MaRDI QIDQ1986529

Zhengzheng Chen, Huijiang Zhao

Publication date: 8 April 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2019.12.029

zbMATH Keywords

strong solutionsnonlinear stabilityrarefaction waveslarge initial perturbationcompressible Navier-Stokes equations with degenerate density-dependent viscosity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Navier-Stokes equations (35Q30) Hyperbolic conservation laws (35L65)

Related Items (3)

Global existence and large-time behavior of solutions to the 1D compressible Navier-Stokes equations with density-dependent viscosity in the half space ⋮ Global strong/classical solutions to the one-dimensional compressible Navier-Stokes-Allen-Cahn system with density-dependent viscosity ⋮ Global stability of rarefaction waves for the 1D compressible micropolar fluid model with density-dependent viscosity and microviscosity coefficients

Cites Work

• Unnamed Item
• Stability of viscous shock waves for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity
• Global existence of strong solution for viscous shallow water system with large initial data on the irrotational part
• Asymptotic stability of viscous shock wave for a one-dimensional isentropic model of viscous gas with density dependent viscosity
• A vacuum problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity
• Global weak solutions to 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity
• The Cauchy problem for 1D compressible flows with density-dependent viscosity coefficients
• Asymptotic behavior of compressible Navier-Stokes equations with density-dependent viscosity and vacuum
• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations
• On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation
• Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas
• Global solutions of the equations of one-dimensional, compressible flow with large data and forces, and with differing end states
• Convergence to travelling fronts of solutions of the \(p\)-system with viscosity in the presence of a boundary
• Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum
• Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model
• Vacuum states for compressible flow
• Shallow water equations: viscous solutions and inviscid limit
• COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY AND VACUUM
• Stability of Rarefaction Waves to the 1D Compressible Navier–Stokes Equations with Density-Dependent Viscosity
• Existence and Uniqueness of Global Strong Solutions for One-Dimensional Compressible Navier–Stokes Equations
• Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas
• Global Existence for 1D, Compressible, Isentropic Navier-Stokes Equations with Large Initial Data
• Global asymptotics toward the rarefaction wave for solutions of viscous 𝑝-system with boundary effect
• Existence of global strong solution for the compressible Navier–Stokes equations with degenerate viscosity coefficients in 1D
• Nonlinear Stability of Strong Rarefaction Waves for Compressible Navier--Stokes Equations
• Non-formation of vacuum states for compressible Navier-Stokes equations
• Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation
• Large-time behaviors of solutions to an inflow problem in the half-space for a one-dimensional system of compressible viscous gas

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